ABSTRACT:Applied mathematical scientists are often faced with the challenge of devising low-dimensional models that capture the essential features of high-dimensional, complex dynamical systems. A common approach is to adopt some low-dimensional equations for a resolved vector and to model the effects of unresolved variables by some kind of noise, the result being a stochastic model. But what if the governing equations for the full system are known and deterministic, even though they are computationally inaccessible?In this talk I will describe an optimization procedure for fitting a canonical statistical model to an underlying dynamics. The resulting closed reduced equations have the generic structure of non-equilibrium thermodynamics. I will also sketch an application of the method to a simplified model of turbulence.

BIO:Bruce Turkington is a Professor in the Department of Mathematics and Statistics, University of Massachusetts, Amherst. He received his PhD in Mathematics from Stanford University in 1978 He was an Assistant Professor at Northwestern University until joining UMass Amherst in 1984. He has been the the Director of the Center for Applied Mathematics for many years, and from 2002 to 2005 he served as Head of the Department.His early research interests lay in the fields of nonlinear partial differential equations and fluid mechanics; specifically, vortex dynamics, nonlinear waves in fluids, and magnetohydrodynamics His more recent work has focused on the statistical mechanics of turbulent fluid flows, especially two-dimensional and geophysical fluids. Currently his research program is directed toward non-equilibrium closure theories for complex dynamical systems.